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- Dynamical Systems With A Continuum Of Randomly Matched Agents

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  • Carlos Alós-Ferrer

    (Universidad de Alicante)

Abstract

Many models postulate a continuum of agents of finitely many different types who are repeatedly randomly matched in pairs to perform certain activities (e.g. play a game) which may in turn make their types change. The random matching process is usually left unspecified, and some Law of Large Numbers is informally invoked to justify a deterministic approximation of the resulting stochastic system. Nevertheless, it is well-know that such laws of large numbers may not hold in this framework. This work shows that there exist random matching processes over a continuum of agents satisfying properties which are sufficient to simplify the analysis of the stochastic system. Moreover, the evolution of the population frequencies of types induced by this system can be described (almost surely) through a set of deterministic equations.

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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-1998-08.pdf
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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 1998-08.

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Length: 31 pages
Date of creation: Apr 1998
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:1998-08

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Related research

Keywords: evolution; random matching; law of large numbers;

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References

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  1. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
  2. Michael Peters, 1995. "On the Equivalence of Walrasian and Non-Walrasian Equilibria in Contract Markets: The case of Complete Contracts," Working Papers peters-95-01, University of Toronto, Department of Economics.
  3. Akihiko Matsui & Kiminori Matsuyama, 1991. "An Approach to Equilibrium Selection," Discussion Papers 1065, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
  5. Gilboa, Itzhak & Matsui, Akihiko, 1992. "A model of random matching," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 185-197.
  6. McLennan, Andrew & Sonnenschein, Hugo, 1991. "Sequential Bargaining as a Noncooperative Foundation for Walrasian Equilibrium," Econometrica, Econometric Society, vol. 59(5), pages 1395-1424, September.
  7. Harrington, Joseph E, Jr, 1998. "The Social Selection of Flexible and Rigid Agents," American Economic Review, American Economic Association, vol. 88(1), pages 63-82, March.
  8. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
  9. Boylan, Richard T., 1992. "Laws of large numbers for dynamical systems with randomly matched individuals," Journal of Economic Theory, Elsevier, vol. 57(2), pages 473-504, August.
  10. Peters, Michael, 1991. "Ex Ante Price Offers in Matching Games Non-steady States," Econometrica, Econometric Society, vol. 59(5), pages 1425-54, September.
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Citations

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Cited by:
  1. Jose A. Garcia-Martinez, 2010. "The Role of Selectivity in Hierarchical Social Systems," Working Papers 2010-05, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
  2. Darrell Duffie & Yeneng Sun, 2004. "The Exact Law of Large Numbers for Independent Random Matching," Levine's Bibliography 122247000000000328, UCLA Department of Economics.
  3. Podczeck, Konrad & Puzzello, Daniela, 2009. "Independent Random Matching," MPRA Paper 27687, University Library of Munich, Germany, revised Sep 2010.
  4. Garcia-Martinez, Jose A., 2010. "Selectivity in hierarchical social systems," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2471-2482, November.
  5. Molzon, Robert & Puzzello, Daniela, 2008. "Random Matching and Aggregate Uncertainty," MPRA Paper 8603, University Library of Munich, Germany.
  6. Vega-Redondo, Fernando, 2000. "Unfolding Social Hierarchies," Journal of Economic Theory, Elsevier, vol. 90(2), pages 177-203, February.
  7. Francesco Squintani, 1999. "Games with Small Forgetfulness," Discussion Papers 1273, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. C. Mendolicchio & D. Paolini & T. Pietra, 2010. "Investments in education and welfare in a two-sector, random matching economy," Working Papers 702, Dipartimento Scienze Economiche, Universita' di Bologna.
  9. Mihaela Schaar & Jie Xu & William Zame, 2013. "Efficient online exchange via fiat money," Economic Theory, Springer, vol. 54(2), pages 211-248, October.
  10. Karavaev, Andrei, 2008. "A Theory of Continuum Economies with Idiosyncratic Shocks and Random Matchings," MPRA Paper 7445, University Library of Munich, Germany.
  11. Molzon, Robert & Puzzello, Daniela, 2010. "On the observational equivalence of random matching," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1283-1301, May.
  12. Carlos Alós-Ferrer & Klaus Ritzberger, 2013. "Large extensive form games," Economic Theory, Springer, vol. 52(1), pages 75-102, January.
  13. Andreas Ramsauer, 1999. "Heterogeneous Discount Factors in an Assignment Model with Search Frictions," Vienna Economics Papers 9807, University of Vienna, Department of Economics.
  14. Matsui, Akihiko & Oyama, Daisuke, 2006. "Rationalizable foresight dynamics," Games and Economic Behavior, Elsevier, vol. 56(2), pages 299-322, August.
  15. Garcia-Martinez, Jose A., 2012. "An Unexpected Role of Local Selectivity in Social Promotion," MPRA Paper 36324, University Library of Munich, Germany.
  16. Carlos Alós-Ferrer, 2000. "Finite Population Dynamics and Mixed Equilibria," Vienna Economics Papers 0008, University of Vienna, Department of Economics.
  17. Russell Golman, 2011. "Why learning doesn’t add up: equilibrium selection with a composition of learning rules," International Journal of Game Theory, Springer, vol. 40(4), pages 719-733, November.
  18. Charalambos Aliprantis & Gabriele Camera & Daniela Puzzello, 2006. "Matching and anonymity," Economic Theory, Springer, vol. 29(2), pages 415-432, October.

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